Field
This invention relates in general to the measurement of liquid-sample volumes and, more specifically, to the use of low-coherence optical interferometry toward that end.
Description of Related Art
In a typical laboratory setting, several small reaction vessels are arranged in a rectangular microplate. These microplates have standardized, common outer dimensions and contain a varying number of vessels, which are referred to as wells. The most common cases are 96, 384, and 1536 wells. The volume of the individual well decreases as the well density of the plate increases. Standardized microplates allow for the use of automated liquid delivery and analysis devices. In many real-world examples, an automatic liquid delivery device is programmed to add specific volumes of various liquids to each of the reaction vessels or wells in a microplate. Subsequently, an automatic analysis device interrogates each of the wells and measures one or several physical or chemical properties. One common example is to read the optical absorbance or emitted fluorescence from each well with a plate reader, but many other measurements are carried out in practice.
In this type of experiment, researchers often derive their knowledge of the volume of liquid added to each well from the instructions sent to the liquid delivery device. Specifically, they rely on the liquid delivery device to add a volume to the well that matches the desired volume as closely as possible. It is, therefore, useful to provide a device whose use enables the independent verification of the performance of the liquid delivery device. In particular, it is useful to provide a device whose use enables the user to independently verify by how much the actually dispensed volume differs from the desired dispense volume. This property is called the accuracy of the liquid delivery device. Similarly, it is important that for the same desired dispense volume, the actual dispense volume exhibit little variation. This property is called the precision of the liquid delivery device.
In practice, automated liquid delivery devices provide for a set of instrument parameters that can be adjusted by the user to ensure that desired dispense volume and actual dispense volume match. Configuring a liquid delivery device for a given experiment by adjusting this set of parameters to ensure accuracy and precision of the liquid delivery device for the specific liquids used in that experiment is one of the most important tasks in reducing the contribution of the liquid delivery device to experimental errors. Typically, a specific set of values has to be chosen for these instrument parameters for each kind of liquid that is being dispensed. Hence, a common industry term for this set of parameters is “liquid class”. Often, instrument parameters also have to be adjusted for dispensing different volume ranges.
The optimal values for this set of instrument parameters may vary from liquid to liquid. This is a result of the physical and chemical properties of the liquid and the configuration of those parts of the liquid delivery instrument the liquid is in contact with. Examples for important aspects of the configuration are pipet and tubing wall materials and dimensions as well as dispense speeds. Among the properties of the liquid that come into play are its surface tension, which describes the interaction with the gas above the liquid, and the interfacial tensions, which describe the interaction with solid materials the liquid comes in contact with. The viscosity of the liquid and the temperature also play an important role.
Currently, researchers use various approaches to verify the performance of liquid delivery devices.
Gravimetric Method for Liquid Volume Measurement
In the gravimetric method, the vessel or microplate is weighed on an analytical balance before and after the sample liquid is dispensed. If the density of the liquid is known, the dispensed volume can then be calculated from the difference in weight.
If this method is to be applied to assessing the errors in liquid delivery into individual wells, a weighing step is performed after each dispense operation, which renders the method very time consuming. In this instance, the change in weight to be measured is also rather small, so that static electricity, drafts, and vibrations, for example, may introduce substantial errors to the measurement.
An alternative common practice is weighing the entire plate before and after liquid is dispensed into each of the wells. This measurement yields information about the mean volume dispensed, but does not offer any information about the precision i.e. the well-to-well variability of the dispensed volume.
Photometric Method for Liquid Volume Measurement
In photometric methods, a liquid solution containing a dye at a known concentration and with known absorbance properties is used as the sample liquid. The measured optical absorbance can then be related to the optical path length in the dye solution, which is equal to the liquid fill height of the well. If the dimensions and shape of the well are known, the liquid volume can then be calculated. This method is limited by the accuracy with which typical absorbance plate readers determine sample absorbance.
A variant of the photometric method, ratiometric photometry is described in U.S. Pat. No. 7,187,455 B2. A system using this approach is currently being manufactured and distributed by Artel of Westbrook, Me. This method involves the use of two different solutions of two different dyes, which aids in obviating some of the limitations of a photometric method based on a single dye. The two different dyes are chosen such that their absorption maxima occur at different wavelengths, so that the absorbance of both dyes can easily be measured simultaneously. The method consists of using a dedicated microplate reader attached to a computer with software to analyze small volumes of pre-calibrated, well-characterized dye solutions that were dispensed into pre-calibrated microplates.
For volume measurements, it is important to take into account the shape of the interface between the liquid sample and the gas above it, its meniscus. In an idealized form, it is assumed to be planar and horizontal. However, in a large proportion of cases of practical relevance, the liquid meniscus is not planar. This deviation from planarity is caused by cohesive and adhesive forces between the liquid molecules, between the liquid and the walls of the vessel, and between the liquid and the gas above it.
Accounting for the shape of this meniscus, however, is useful to increase the accuracy of the liquid volume measurement. If the meniscus is curved, measuring the liquid fill height at one point in the well is no longer sufficient to determine the volume of the liquid. Importantly, the shape of the meniscus may vary with the composition of the liquid and the material of the microplate. In the ratiometric photometry method described in U.S. Pat. No. 7,187,455 B2 the user is limited to specific liquids that have undergone extensive characterization. In practice, the user purchases these solutions from the manufacturer. U.S. Pat. No. 7,187,455 B2 states that these liquids are composed in such a way as to ensure that the meniscus remains very close to planar to ensure the shape of the meniscus does not introduce unacceptably large errors into the volume measurement.
In cases where a user wants to rapidly verify the level of accuracy and precision for a given experimental liquid and the liquid class parameters chosen for this specific experiment, the method described in U.S. Pat. No. 7,187,455 B2 does not provide a convenient solution. Examples for cases such as this are liquids that contain detergents, plasma, or organic solvents, among others.
Further, the method described in U.S. Pat. No. 7,187,455 B2 does not provide a convenient solution for a user who wants to measure the volume of liquid in a plate and then subsequently use that same liquid in an unaltered state for an experiment. The presence of dyes in this method makes this impossible.
Ultrasonic Ranging for Liquid Volume Measurement
A number of commercially available instruments use ultrasonic ranging to sense the elevation of the liquid meniscus. Instruments of this type are the BeeSure manufactured by Bionex Solutions Inc. of Sunnyvale, Calif., and the VolumeCheck 100 by BioMicroLab of Concord, Calif. In one embodiment, a transducer is moved above the well. A pulse of ultrasonic energy is directed toward the surface of the liquid. A fraction of the ultrasonic energy is reflected towards the transducer, where the time of its arrival is measured. The time-of-flight between when the original pulse leaves the transducer and when the reflected pulse impinges on it is related to the distance traversed and the speed of sound in the gaseous medium above the liquid. Upon proper calibration, measuring this time can, therefore, yield the elevation of the meniscus in the well, which in turn is related to the liquid volume contained in the well. Due to inherent limitations in the distance resolution of ultrasound measurements, this method is suitable to detect the presence of liquid in a well, but the resolution is not high enough to measure liquid volumes with sufficient resolution for the needs of many liquid delivery applications. Further, methods relying on ultrasound focus the sensing ultrasonic wavefront into the well of a microplate. For small wells, the ultrasonic wavefront suffers diffraction at the opening of the well, and depth information cannot be recovered from the reflection. This also limits the usefulness of this method for microplates with smaller wells at higher density.
Ultrasonic Ranging in Instruments for Acoustic Liquid Transfer
In another type of commercially available instrument, ultrasonic energy is focused through the bottom of the well. The main purpose of this type of instrument is the transfer of very small droplets of liquid from one microplate into another microplate. As a side product of pursuing this objective, these instruments can also provide a measurement of the liquid fill height. Instruments of this type are manufactured by Labcyte Inc. of Sunnyvale, Calif. and by EDC Biosystems of Fremont, Calif.
In these instruments, a transducer is acoustically coupled to the bottom of the microplate with a water jet. A pulse of ultrasonic energy is triggered and travels through the plate and the liquid until it is reflected at the underside of the liquid meniscus, the liquid-air interface. It then travels back through the liquid and the plate to the transducer, where its arrival is recorded. Given the speed of sound in the liquid, the fill height of the liquid in the well can be determined from the time-of-flight between when the pulse left the transducer and when its reflection impinges upon it.
The utility of this method for routine calibration is limited because the liquid delivery device is very expensive and requires plates of a specific material. Its resolution is limited by the inherent resolution limit of ultrasonic ranging.
Seal-and-Pressurize Method for Liquid Volume Measurement
In another commercially available method, the individual wells of the microplate are connected to individual gas reservoirs of adjustable volume such as syringe-like devices in such a manner that they are sealed by a gasket. An instrument of this type is manufactured by Stratec Biomedical AG of Birkenfeld, Germany. In a sealed chamber such as this which cannot exchange gas with the outside, the pressure of the gas is related to the volume of the chamber by a known relationship. As the volume in the newly connected outside reservoir is reduced, the pressure in the sealed chamber, therefore, rises. Because the liquid is incompressible, knowledge of the change in pressure for a given change in volume, therefore, allows for the determination of the gas volume in the well. By definition, the proportion of the total well volume that is not taken up by gas is taken up by liquid, and the volume of liquid in the well can thus be determined.
Challenges that limit the utility of this method in a laboratory setting include the fact that the gas pressure in the sealed chamber also depends on the temperature. Unless temperature is carefully controlled, it is a major error source.
Second, sealing each well of the plate to its corresponding piston is accomplished by a gasket that touches the top rim of the well, which bears the risk of contamination of the contents of the well.
Fluorescent Dye Method for Liquid Volume Measurement
Another method used by practitioners consists of dispensing a solution of a fluorescent compound. Each well can then be read with a plate reader to determine the amount of fluorescence emitted and thus the amount of liquid dispensed into the well. Measurements of this type are notoriously difficult to calibrate.
Optical Interferometry
Interferometry is a well-known technique that uses the wave nature of light to measure distances. De Groot gives an overview of its use in the measurement of surface topography.
In one typical arrangement, light emanating from a light source is split into two beams by a beam splitter. One of these two beams, the sample beam, is directed towards a surface of interest, and the other beam is directed towards a reference surface. Upon reflection at the surface of interest, the reflected sample beam travels back towards the beam splitter. The beam traveling towards the reference surface is reflected there and also travels back towards the beam splitter. The beam splitter then recombines these two beams and directs them to a detector configured to detect the intensity of incident light.
The intensity that is recorded by this detector is dependent on the phase relationship between the two beams after they have been recombined by the beam splitter. The phase relationship, in turn, is determined by the optical path length difference between the paths from the beam splitter to the respective surfaces. The optical path length of a beam is the product of the refractive index of the medium and the geometric distance the beam has traveled. If the optical path length difference is an integer multiple of the wavelength, the beams are said to interfere constructively and the detector will see an irradiance maximum. If the optical path difference however is an odd multiple of half the wavelength, the beams will interfere destructively and the detector will see an irradiance minimum. An analysis of this pattern of irradiance minima and maxima yields information about the relative optical path length difference between the sample beam and the reference beam.
Low-coherence Optical Interferometric Ranging
The phenomenon of interference between two beams is observable for a limited range of path length differences between the two beams. The characteristic attribute of a light source that describes this property is the coherence length, which is a measure of the path length over which the phase relationship of a beam remains stable. Hence, it characterizes the range of path-length differences over which interference can be observed. The coherence length of a light source is inversely proportional to its spectral bandwidth. For light sources with a high coherence length and narrow spectral bandwidth, such as some lasers, an interference pattern can be observed even for relatively large path-length differences, whereas for light sources with a broader emission spectrum the coherence length is substantially shortened, and interference can only be observed across a narrow range of path length differences. It is because of this presence of interference across a relatively narrow range of path-length differences that this type of broadband light sources with limited coherence length can be used to determine the distance to a reflective surface. Examples for such broadband light sources include light-emitting diodes, superluminescent diodes, incandescent bulbs, and arc lamps.
This is the principle of the well-known technique of low-coherence interferometric ranging. A low-coherence optical interferometric ranging system (LCOIRS) is a system that uses this approach to determine the distance to a reflective surface. A low-coherence Michelson interferometric ranging system (LCMIRS) relies on a Michelson interferometer to split, recombine and observe the optical path length difference between sample beam path and reference beam path. Low-coherence interferometric ranging is widely used in materials science and other disciplines to non-invasively determine the shape of reflective surfaces, such as the surfaces of optical elements or of semiconductor materials.
Sample Quantity vs Sample Properties.
There is potential for confusion in the context of optical technologies used to study liquids. Optical technologies are widely used to study the internal properties of liquids by passing optical beams through the interior of the liquid sample. The present invention is not concerned with the internal properties of the liquid sample, does not rely on light penetrating the sample, and is designed to be independent of the internal properties of the sample, which can remain unknown. We are concerned here exclusively with the use of optical-interferometric ranging to determine the position in space of the exterior, volume-defining, free surface of a liquid sample.
U.S. Pat. No. 5,323,229 by May discloses a device to measure the thickness of a transmissive sample. The sample attribute measured by the device described in U.S. Pat. No. 5,323,229 is the optical thickness, the product of the refractive index of the sample and the physical thickness of the sample. U.S. Pat. No. 5,323,229 describes a variety of means to obtain the physical thickness of the sample from the optical thickness, either by obtaining the refractive index of the sample in an independent measurement, or by placing the unknown sample into one arm of the interferometer and a standard of the same refractive index and defined thickness into the other arm of the interferometer. In the case of liquid samples such as films, U.S. Pat. No. 5,323,229 discloses a method of confining an additional aliquot of liquid in a cuvette of defined path length to this end. While this is of great utility in the assessment of the thickness of films of liquid produced in industrial quantities, the need to use additional liquid merely for the independent compensation of the sample's unknown refractive index makes this method inconvenient and impractical to use in the case of scarce and precious samples, as they are routinely encountered in life sciences laboratories.
U.S. Pat. No. 7,233,391 (B2) by Schermer describes a device and method to determine internal properties of a liquid sample confined in the wells of a microplate, such as the refractive index of the liquid, or molecular interactions between molecules immobilized on a container surface and analyte molecules in the liquid.
U.S. Pat. No. 6,958,816 (B1) by Dogariu discloses devices and methods to use dynamic light scattering to determine internal properties of liquids, in particular their rheological properties, such as their complex shear modulus, elasticity, viscosity, and viscoelasticity. While Dogariu's approach exploits optical interference between two beams, the sample beam results from reflections at particles suspended within the sample, rather than from a reflection at the sample surface, as in the present invention. The devices described in Dogariu determine the thermal motion of particles suspended in solution to deduce rheological properties rather than the position of the liquid surface to deduce the sample volume, the focus of the present invention.
U.S. Pat. No. 8,934,104 (B2) by Koerner illustrates the use of a device and method to apply optical interferometry to determine properties of biological or technical material over an unspecified sample volume. In the devices described by Koerner, an optical beam is reflected at the sample surface or within the sample to measure properties including the distance, depth, profile, form, undulation, roughness, optical thickness, and deviation from flatness. Koerner does not address the focus of the present invention, the sample volume.